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Ministry of Higher Education

Kingdom of Saudi Arabia CSTS

SEU, KSA Discrete Mathematics (Math 150)

Level III, Assignment 2

(2015) 1. State whether the following statements are true or false: [9] (a) Two sets are equal if and only if they have the same number of elements.

(a)

(b) If A is a proper subset of B then the cardinality of A and B are same.

(b)

(c) If two sets are disjoint then their intersection is not an empty set.

(c)

(d) If range and codomain of a function f are equal then f is a surjective function.

(d)

(e) If f is not bijective then f can not be invertible.

(e)

(f) In an algorithm, in?nite number of steps may be used to get the desired output.

(f)

(g) If a 24-hour clock read 18:00, then after 95 hours it will read 17:00.

(g)

(h) Every prime number is not even.

(h)

(i) The integers 12, 17 and 21 are pairwise relatively prime number.

(i) Page 1 of 3 Please go on to the next page. . . Math 150 Department of Mathematics 2. Select one of the alternatives from the following questions as your answer.

(a) If A = {1, 7, 9, 15} then the number of possible subsets of A are

A. 12

B. 16

C. 8

D. 6

(b) If A = {1, 3, 5, 7, 9, . . .} with the set of positive integers as the universal set. Then

A is

A. Set of positive even integers

B. Set of negative even integers

C. Set of negative integers

D. None

(c) If f : A ? B be a function such that f (a) = 4, f (b) = 1, f (c) = 2 and f (d) = 5

where A = {a, b, c, d, } and B = {1, 2, 3, 4, 5, 6} then

A. f is 1-1 and onto both.

B. f is onto but not 1-1.

C. f is 1-1 but not onto.

D. f is not a function.

(d) If f : A ? B, g : B ? B and h : B ? A are functions then composition function

gof be a function from

A. A ? A

B. B ? A

C. B ? B

D. A ? B

(e) If f : Z ? Z be a function such that f (x) = 2x, then

A. f is 1-1.

B. f is onto

C. f is bijective

D. All of the above

7 (f) The value of (?1)j is j=4 A. 0

B. 1

C. -1 Page 2 of 3 Please go on to the next page. . . [9] Math 150 Department of Mathematics

D. 2 (g) Which of

A.

B.

C.

D. the following is NOT true:

12 ? 4( mod 2)

17 ? 7( mod 10)

104 ? 91( mod 12)

210 ? 10( mod 5) (h) The value of the modular expression (7 +11 10) .11 (9 +11 6)

A. 255

B. 2

C. 4

D. 6

(i) If G.C.D(a, b) = 10 and ab = 40 then L.C.M (a, b) =

A. 400

1

B.

4

C. 4

D. 1 3. If A = {1, 2, 3, 7, 9, 11, 14, 15, 16}, B = {1, 7, 11, 13, 19} and C = {2, 4, 6, 8, 10, 11, 12, 19},

then show that

A ? (B ? C) = (A ? B) ? (A ? C). [2] 4. If f, g : Z ? Z be functions such that f (x) = 3x + 2 and g(x) = 2x2 + 1, then ?nd the

values of (gof )(x) and (f og)(x). [2] 5. If an = an?1 + an?2 with a0 = 1, and a1 = 2, then ?nd the value of a5 of the given

sequence. [2] 6. List all the steps used to search for 9 in the sequence 1,3,4,5,6,8,9,11 using linear search.

7. Find the octal expansion of (765)10 . [2] 8. Find the greatest common divisor of 314 and 520 by using the Euclidean Algorithm. [2] Page 3 of 3 End of Assignment.

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